JOURNAL OF SCII NCH OH HNUH 2012, Vol 57 No 10,pp, S 13 DAY HOC M() RONG KHAI NIEM SO MU CUA LUY THt/A d LCtP 12 TRUNG HOC PHO T H O N G (BAN NANG CAO> I HEO QUAN DIEM CtJA LY TIIUYlVl HNH HUONG Nguyd[.]
JOURNAL OF SCII-NCH OH HNUH 2012, Vol 57 No 10,pp, S-13 DAY HOC M() RONG KHAI NIEM SO MU CUA LUY THt/A d LCtP 12 TRUNG HOC PHO T H O N G (BAN NANG CAO> I HEO QUAN DIEM CtJA LY TIIUYlVl HNH HUONG Nguydn Manh Cang Tnfffng Dgi bgc Supham Hd Ntfi Hmail: nguyenmanhcangdhsp@yahoo.com Tom lil Tfl SLf phan Ifch c;ic nid rdng khiii nifim sd mu cua luy thfla ve cac mat loan hoc Ljch sfl Toan hpc va Ly luan Day boc Toan, tren cd sd nhflng tri thflc, nhflng phUdng phap cua Ljch sfl Toiin hoc Ly luan Day hoc Toan bai bao xay dung mol linh hudng IUdng Ihich de day hpc md rong khai niem sd mu cua luy thfla vdi hy vpng tinh hudng nhU vay, hpc sinb la chu the xay dung tri tbflc can hoc Tifkhda: So mu Ly luan Day bpc Toan ly thuyet tinb hudng Mb dau Hoc sinb ldp 12 (ban nang cao) kbi hoc: Luy thfla vdi sd mu hflu ti da gap cac dinh nghia sau: "Vdi a / 0, n = hoac n la mot sd nguyen am, luy thfla bac n cua a la sd o" xac dinh bdi a° ~ 1, o" = ", va "Cbo a la mot sd thflc dfldng va r la mdt sd hflu ti a'" Gia sfl r = -~ dd m la mot sd nguyen, cdn n la mpt sd nguyen dfldng Khi do, liiy T77 thfla cua a vdi sd mu r la sd a*" xac dinh bdi a*" = a " = >/«^ " [4] Hpc sinh da gap a" la mpt ticb cua n thfla sd bang a: a" = a.n n (n thfla sd), vdi n nguyen dfldng, den nay, kbi gap a", a"'', a a hpc sinh khong khoi la lam va dot ngpi Cac em tiep thu cac dinh ngbia tren cd phan khien cfldng vi chfla hieu dfldc y nghia cua chung Ve pbia ngfldi day, mac du mudn ndi ve y nghia ciia cac dinh nghla noi tren nhflng cung gap khd khan phai giai tbich d thdi diem nay, ma cho rang hpc sinh se hieu cac dinh ngbia qua trlnb hpc bam sd mu vd sau Day la mpl thflc trang ma bien v5n phai chap nhan Van de dat la, cd the khac phuc thflc trang khong? Cau tra ldi la cd the! Noi dung nghien cihi Ve mat toan hpc, d dSy ta gap bai toan vd md rpng mien xac dinb cua ham sd mu y = a''{a > 0, a 7^ 1) tfl chd ham sd co tSp xac dinh ia tap cac sd nguyen dfldng, tdi Day hgc md rgng khdi niem sd nm ciia Idy thifa d Idp 12 chd cd lap xac dinh lan IflOl la tap cac sd nguyen, rdi lap bpp cac sd hflu ti va tdi lap sd thllc,, Viec md rpng phai thda man cac yeu cau nhat dinh dfldc quy dinh bdi muc dfch nghien cflu va cac djnh nghia tfldng chflng nhfl cd phan khien cfldng neu tren, chinb la ket qua tSt ydu cua viec gijii bai loan nay, Trong Lich sfl Toan hpc [2], vice md rpng khai niem sd mu ciia lijy thfla da dfldc quan tam tfl vkt lau, vdi muc dich lim tdi phfldng phap va cac cdng cu tfnh loan Dc dfla mpt phep loan vd mpt phep loan ddn gian hdn, chi c5n lap bang ddi chieu day cac IQy ihfla Clia cac sd vdi day cac sd mu cua chung Di^u dan den vice so sanh hai cap so: cap sd cpng va cap sd nhan, md rdng cho d5y dii khai niem liiy thfla Xuat phal lfl quan dicm tren, dua phan sd xen ke cac sd tfl nhien vao cap sd cdng, 6-rcl da den vdi cac luy thfla vdi sd mu phan, licp dd Sti-phen da den vdi luy Ihfla vdi so mu phan va am [2], Ve mat ly luan day bpc [ 1,3J, de day mdt iri tbflc Toan bpc, ly thuydt linb hudng cho r5ng cSn phai de hpc sinh sdng boan canh ma tri thflc dd dupc sinh, vay de day mdl tri thflc va mudn lot la dflpc y nghia cua nd, giao vicn phai hoan canh hda tri ibflc sach giao khoa, de hoan canh dd, bpc sinb lao kidn thflc mdi ma la mong mudn Di/di day la qua trmh xay dung mdt tinh hudng Ifldng tbich dc day hpc khai niem luy thfla vdi by vpng, linh budng nhfl vay, bpc sinh la chii the xay dflng Iri tbflc c5n hpc, va tbflc trang neu d phan dau bai viet se dUdc khac phuc Hogt dgng I: Cho day sd: 1,2,3,4, (1) , , , 16, , , { ) Hpc sinh: - Nhan dang bai day sd Ket qua: (1) la mdt cap sd cdng U\ = \.d = \, cdn (2) la mdt cap sd nban Vi = 2.q = - Tim mdt each cbo Ifldng flng mdi sd hang cua day sd (1) vdi mpt sd hang nbSt cua day sd (2) Ket qua: L 3, 4, n l l i i i 21 2^ 2^ 2'^ T Giao vien: Nhfl vay cbung ta da cd dflpc mpl Hinh Do thi hdm sdy = 2^ ham sd tren tap xac dinb la tap hdp cac sd nguyen tren tap xdc dinh {1,2,3} dfldng, ham sd dfldc ky hieu la: y — 2^ vdi X e N+ va dflpc gpi la ham sd mu tren tap hdp cac sd nguyen dflpng Hoc sinh: Ve dd thi cua ham sd y = 2^ trSn tap xac dinh {1,2,3} {Hinb 1) Do tbi gdm Nguyen Manh Ciing dicm 1(1, 2); (2,4); (.1,8)) Iloat dong 2: Giiio vicn: la md rpng day so (I) bing each vicl licp Ian lUpl cac so hang 0,-1,-2, -.1 ttl phiii sang trai (0 lien kc 1) la dupc mot cap so cpng md rpng vo han ca ve hai phia kV hicu lil (!') -2 -1.0 1,2, ( D Hoc sinh: Md rpng cap so nhan (2) dc co mpl cap so nhan mfl rpng (2') bjng each cho IUdng ling mni so hang ciia diiy (1') vdi mpt so hang nhSt cOa (2'), td'c la phai di6n s() Ihich hpp vao vi iri dau ?: ,-.^.-2.-1,0, 1.2,.3 (1') , ?, '.' '.' 21, 22 2^ Cap so nhan md rpng cd cong bpi bang 2, nd cd dang sau: , , - .1.2, I.X., , viicdthcvietdudidang ,—.—.-7 1,2',2^2', (2') ,s 2.1 22 2' Giao vien: Ta cd sU IUdng iJng giiia cac so hang cua ( D va (2') nhu sau: 1 -2 -1 - 'I -> H -> 2' 0-*22 0->2' Nhu vay la chiing ta da cd ~^ :iS J» dupc mpt ham s6 xac dinh tren tap Hinh Do thi ham soy = 2' hpp s6 nguyen ky hieu la 1/ = 2' tren lap xdc tiinh (-3, -2, -1, 0,1,2} vdi e Z dupc gpi la ham so mu tren tap hop so nguyen: 2'" = ^ ^ neu X = m nguyen dUOng •/ -•2'- neu X = neu X m Hoc sinh: Ve thi Clia ham so y = 2* tren tap xac dinh -3, -2, -1, 0, I, (Hinh 2) Dgy hgc md rimg khdi niim so mu cua luy thifa d It'fp 12 ^^o Ihi c k ve di qua diem sau: ( ( -3 \)- (-2, \)] ( - i ) ; (0 i); {1-2}: (2.4} i L S J Hogt dgng 3: Gido vien: Ta md rpng cap sd cpng (T) bang each viel xen vao gifla hai so hang lien tiSp cua nd mpt sd hang mdi cho cap sd cpng mdi cd cdng sai bang -, ky hicu la(r') 1 ,-3.-5 -2,-5,-i. .a-,i,^.2.j.3, (r) ^ Hoc sinh: Hay md rdng cap sd nhan (2") de cd mdt cap sd nban md rpng bang each cho tlidng flng mdi sd bang ciia (1") vdi mpl sd hang nhal cua (2"), lfle la phai dicn sd tbi'ch hdp vao vi tri dau? _ - : - ? - i i.n,i.i.^.2.|3 a", ?_7-?l?2"?4?S 8' " ' " 2' •• ' CSp s6 nhan mfl rpng cd cong bpi bSng \/2, nd cd dang sau: .,^.^,^,.^.l.'/2K^ -J^ V¥ (2") \/2l \/23 ^2^ ^ Giao vien: Ta cd su tudng Ung giiia cac s6 hang ctia (1") va (2") nhu sau: ^3 "2^7P 2j JV 0->l (3 day cbung la da cd bam sd mu t/ = 2^ xac dinb tren tap bpp gdm cac sd hflu ti dang ±— vdi m G Z Hogt dgng 4: Gido vien: Ndu ta md rpng cap sd cpng (1") bang each viet xen vao gifla hai sd hang lien tidp mpt sd cac sd hang mdi cbo cap sd cpng met rdng cd cdng sai bang — (n nguyen dfldng Idn hdn hoac bang 2) thi cap so nban md rpng tfldngflngse cd cdng bpi bang \/2 Luc sfl tfldngflnggifla cac sd bang eua bai §p sd ndi tren se la: Nguyin Manh Ciing n "2 7, n *-^ >w1 'W )-> y? ll - -> y j j Den day chiing ta da cd hiini so mu vfli tap xac dinh cua nd lii lap hpp so hihi li Q, duoc gpi la hiim sd mii i/ = 2' tren tap hdp so hiiu li: ' 2 neu I - m nguyen dUPng neu V = !J = ' = < " „, neu I = Hoc sinh: Ve dd thi cua bam sd y 2-^ tren tap xac dinb { - , —- , ^ , } Dd thi can vc di qua diem sau: , ^ ) : ( , i ) ; ( i v^):(1.2):(-,v/2J):(2, 1) • ' " "2' (-i.^);(- iloat dpng 5: Giao vien: - Chiing la da xuat phat ttt ham so mu 1/ = ' vfli tap xdc dinh la tap cac so nguyen dUPng N"*", ta da lan lupt mfl rpng cac mien xac dinh cua nd de tuong iing cd ham so y = 2* tren tap so nguyen, roi tren tap hpp so hUu ti Ham so mfl rpng se trung vdi ham so cu xet nd tren mien xac dinh ban dau cQa no Viec lam gpi la thac trien mpt ham sd Ciing vfli viec thac trien nay, nhting sU tuong quan mfli giiia cac so thupc mien xac dinh va mien gia tri ciia ham sfl dupc xac lap: cac ky hieu tnlflc day vo nghla, da cd nghia xac dinh, diSu dupc gpi la su mfl rpng khai niem so mii cua luy thita Viec thac trien ham so mii t/ = a-'(a > 0, a / 1) tiin hanh tUOng tu nhu vfli y = 2' Dgy hgc md rimg khiii niim sd mii cua IQy thifa d ldp 12 - Viec thac trien ham sd mu y = a ' ( a > O.a f- 1) se ddng hanh vdi vice phat Irien khai niem sd Trong pbam vi chfldng trinh ldp 12 la da cd kbai niem ve ham sd mu y = a'^(a > 0,a^ 1) tren tap xac dinh ciia nd la tap hdp sd Ihflc R Vice xay dflng bam sd gan lidn vdi vice md rpng kbai niem sd mu ciia luy Ihfla sd mu la sd vd ti' Hoc sinh: Tfl dpc hieu hai ndi dung [4;53-54]: - Luy thfla vdi sd mu vd li - Ticb chat luy thfla vdi sd mu thuc Ket luan Bai bao da chi nhflng net cdn khien cfldng bpc sinb du:pc irang bi nhflng kidn thflc ve bam sd mil, Bai bao da Ihiet ke dfldc tinh hudng day bpc khai niem ham sd mu dua tren pbfldng dien Toan hpc, Lich sfl Toan bpc va Ly luan day hpc mon Toan cd the khac phuc nhflng khien cfldng dd TAI LIEU THAM KHAO [I] Brousseau G., 1986 Fondements el methodes de la didactique des RDM Vol 72 matbematiques [2] K A Rflp-ni-cdp, 1967 Lich su Todn hgc (Vu Tuan dich), Nxb Giao due Ha Ndi [3] Nguyen Manh Cang, 1999 Xdy dung linh hudng dgy hgc dinh ly Talet Thdng bao Khoa hpc - Dai hpc Qudc gia Ha Npi, Trfldng Dai hpc Sfl pham sd [4] Gidi tich 12 [ndng cao) Nxb Giao due Viet Nam, 2011 ABSTRACT Creating teaching situations in which exponential functions can be taught to grade 12 high school students This article proposes several means of teaching exponential functions which make use of an analysis of mathematical, historical and methodological aspects of exponential functions and current knowledge, methods of mathematical history and mathematical methodology in order to teach students to learn the concepts by themselves ... hpc Sfl pham sd [4] Gidi tich 12 [ndng cao) Nxb Giao due Viet Nam, 2011 ABSTRACT Creating teaching situations in which exponential functions can be taught to grade 12 high school students This... niim sd mii cua IQy thifa d ldp 12 - Viec thac trien ham sd mu y = a '' ( a > O.a f- 1) se ddng hanh vdi vice phat Irien khai niem sd Trong pbam vi chfldng trinh ldp 12 la da cd kbai niem ve ham... ti Ham so mfl rpng se trung vdi ham so cu xet nd tren mien xac dinh ban dau cQa no Viec lam gpi la thac trien mpt ham sd Ciing vfli viec thac trien nay, nhting sU tuong quan mfli giiia cac so